By: Isaac Newton

Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion ...

By: Dr. José Anson; Joëlle Toledano Bialot

This book examines the economics of the postal sector through three lenses: snapshot and trends, models, and opportunities. In the years to come, the Universal Postal Union plans to develop its role as a knowledge centre for the postal sector from these perspectives.
At this time of radical transformation of the postal sector, it is important to understand how the sector has evolved historically, how it is connected with the economic system, and where it is heading. T...

By: Surajit Basu

This is a collection of puzzles requiring in most cases – high school math.
The purpose is not necessarily to solve these problems, but to get you to think about different types of math puzzles. Many of the puzzles are introductions to different areas of math.
Most of these puzzles can be done mentally. If you have to write, expect to write no more than a page. Pictures are useful.

“There are three planes”, said Onko, “which take off simultaneously - from Bangalore, Athens, and New York.”
“Each plane goes 500 km north, then 500 km east, then 500 km south, and then 500 km west.”
“Which plane is closest to its starting point?”, said Onko with a smile.

By: A.A.K. Majumdar

In writing this book, the first problem I faced is to choose the contents of the book. Today the Smarandache Notions is so vast and diversified that it is indeed difficult to choose the materials. Then, I fixed on five topics, namely, Some Smarandache Sequences, Smarandache Determinant Sequences, the Smarandache Function and its generalizations, the Pseudo Smarandache Function and its generalizations, and Smarandache Number Related Triangles. Most of the results appea...

By: Florentin Smarandache; W. B. Vasantha Kandasamy

This book has five chapters. In Chapter I, we give a brief description of the sixteen sutras invented by the Swamiji. Chapter II gives the text of select articles about Vedic Mathematics that appeared in the media. Chapter III recalls some basic notions of some Fuzzy and Neutrosophic models used in this book. This chapter also introduces a fuzzy model to study the problem when we have to handle the opinion of multiexperts. Chapter IV analyses the problem using these mode...

We then remove the common factor if any from each and we find x + 1 staring us in the face i.e. x + 1 is the HCF. Two things are to be noted importantly.
(1) We see that often the subsutras are not used under the main sutra for which it is the subsutra or the corollary. This is the main deviation from the usual mathematical principles of theorem (sutra) and corollaries (subsutra).
(2) It cannot be easily compromised that a single sutra (a Sanskrit word) can be mathemat...

By: Florentin Smarandache

Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind combined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit.
...

After the experiments were completed, the life span of such “atoms” was calculated theoretically in Chapiro’s works [61,62,63]. His main idea was that nuclear forces, acting between nucleon and anti-nucleon, can keep them far away from each other, hindering their annihilation. For instance, a proton and anti-proton are located at the opposite side of the same orbit and move around the orbit’s centre. If the diameter of their orbit is much larger than the diameter of the ...

By: Shaanxi Xi'an

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

An identity involving the function ep(n)
Abstract The main purpose of this paper is to study the relationship between the Riemann zeta-function and an in¯nite series involving the Smarandache function ep(n) by using the elementary method, and give an interesting identity.
Keywords Riemann zeta-function, in¯nite series, identity.
x1. Introduction and Results
Let p be any fixed prime, n be any positive integer, ep(n) denotes the largest exponent of power p in n. Th...

By: Shaanxi Xi'an, Editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

A structure theorem of right C-rpp semigroups1
Abstract A new method of construction for right C-rpp semigroups is given by using a right cross product of a right regular band and a strong semilattice of left cancellative monoids.
Keywords Right C-rpp semigroups, right cross products, right regular bands, left cancellative monoids.
x1. Introduction
Recall that a semigroup S is called an rpp semigroup if all its principal right ideals aS1,
regarded as right S1-sy...

By: Shaanxi Xi'an, Editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

Abstract In this paper, we use 4-cyclotomic cosets of modulo n and generator polynomials to describe quaternary simple-root cyclic codes of length n = 85. We discuss the conditions under which a quaternary cyclic codes contain its dual, and obtain some quantum error-correcting codes of length n = 85, three of these codes are better than previous known codes.
Keywords Quaternary cyclic code, self-orthogonal code, quantum error-correcting code.
x1. Introduction
Sinc...

By: Shaanxi Xi'an, Editor

This issue of the journal is devoted to the proceedings of the third International Conference on Number Theory and Smarandache Problems. The conference was a great success and will give a strong impact on the development of number theory in general and Smarandache problems in particular. In this volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type probl...

Abstract : Let k be any ¯xed positive integer, n be any positive integer, Sk(n) denotes the smallest positive integer m such that m! is divisible by kn: In this paper, we use the elementary methods to study the asymptotic properties of Sk(n), and give an interesting asymptotic formula for it.
Keywords : F. Smarandache problem, primitive numbers, asymptotic formula.

By: Shaanxi Xi'an, Editor

In the volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems. There are a few papers which are not directly related to but should fall within the scope of Smarandache type problems. They are 1. L. Liu and W. Zhou, On conjectures about the class number of binary quadratic forms; 2. W. Liang, An identity for Stirling numbers of the second kind; 3....

On Algebraic Multi-Vector Spaces
Abstract A Smarandache multi-space is a union of n spaces A1;A2;An with some additional conditions hold. Combining these Smarandache multi-spaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces is introduced. Some characteristics of multi-vector spaces are obtained in this paper.
Keywords Vector, multi-space, multi-vector space, dimension of a space.
x1. Introduction
These multi-spaces was ...

By: Shaanxi Xi'an, editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

x1. Introduction
The study of Smarandache loops was initiated by W.B. Vasantha Kandasamy in 2002. In her book [19], she defined a Smarandache loop (S-loop) as a loop with at least a subloop which forms a subgroup under the binary operation of the loop. For more on loops and their properties, readers should check [16], [3], [5], [8], [9] and [19]. In her book, she introduced over 75 Smarandache concepts on loops. In her ¯rst paper [20], she introduced Smarandache : left(...

By: Shaanxi Xi'an, Editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

0. In 1999, the second author of this remarks published a book over 30 of Smarandache's problems in area of elementary number theory (see [1, 2]). After this, we worked over new 20 problems that we collected in our book [28]. These books contain Smarandache's problems, described in [10, 16]. The present paper contains some of the results from [28]. In [16] Florentin Smarandache formulated 105 unsolved problems, while in [10] C.Dumitresu and V. Seleacu formulated 140 unso...